Question

find the sum of first 15 natural numbers​

Answer 1

Step-by-step explanation:

step 1 address the formula, input parameters & values.

Input parameters & values:

The number series 1, 2, 3, 4, . . . . , 14, 15.

The first term a = 1

The common difference d = 1

Total number of terms n = 15

step 2 apply the input parameter values in the formula

Sum = n/2 x (a + Tn)

= 15/2 x (1 + 15)

= 240/2

1 + 2 + 3 + 4 + . . . . + 14 + 15 = 120

Therefore, 120 is the sum of positive integers upto 15.

Answer 2

SOLUTION

TO DETERMINE

The sum of first 15 natural numbers

EVALUATION

Here first 15 natural numbers are

1 , 2 , 3 , 4 , . . . . , 15

This is an arithmetic progression

First term = a = 1

Common Difference = d = 1

Number of terms = 15

Hence the required sum

$\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }$

$\displaystyle \sf{ = \frac{15}{2} \bigg[ (2 \times 1) + (15 - 1)\bigg] }$

$\displaystyle \sf{ = \frac{15}{2} \bigg[ 2 + 14\bigg] }$

$\displaystyle \sf{ = \frac{15}{2} \times 16 }$

$\displaystyle \sf{ = 15 \times 8}$

$\displaystyle \sf{ = 120 }$

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